What are the coordinates of the point on the directed line segment from (5, -5)(5,−5) to (7, 7)(7,7) that partitions the segment into a ratio of 3 to 1?

The coordinate of the point on the line segment from (5, -5) to (7, 7) that partitions the segment into a ratio of 3 to 1 is (6.5, 4)

Step-by-step explanation:

Here we have the points on the line given as

(5, -5)  and  (7, 7)

Therefore to the distance between the x and y coordinates are;

x-coordinate difference,  7 - 5 = 2 and

y-coordinate difference,  7 - (-5) = 12 and

The required ratio is 3:1, that is 3 portions on one side and 1 portion on the other.

Therefore, the total portion of the line is 3 + 1 = 4

So we divide each of the differences between x and y by 3/4 and add it to the coordinate of the first point on the line as follows

x-coordinate difference × 3/4 = 2×3/4 =1.5

y-coordinate difference × 3/4 = 12×3/4 = 9

Therefore, the coordinate of the point on the line segment from (5, -5) to (7, 7) that partitions the segment into a ratio of 3 to 1 is

x-coordinate = 5 + 1.5 = 6.5

y-coordinate = -5 + 9 = 4

or (6.5, 4).

hope it you

step-by-step explanation:

sin(7pi/6 - pi/3)  

= sin(7pi/6 - 2pi/6)  

= sin(5pi/6)  

= sin(pi - pi/6)  

= sin(pi/6)  

= 1/2  

sin 7pi/6 - sin pi/3  

= sin (pi + pi/6) - sin pi/3  

= -sin pi/6 - sin pi/3  

= -1/2 - sqrt(3)/2  

= -(1+sqrt(3))2